The concept of employing a plurality of spheres disposed within a toroidal cavity connecting a flow inlet to a flow outlet, wherein the spheres undergo an orbiting movement through the toroidal cavity with cross section closely matched to the dimension of the spheres, is a very neat idea that can bring forth an elegant positive displacement fluid handling device. The problem with this concept is that none of the existing arts employing the principles of the spheres orbiting through the toroidal cavity works in reality, which nonworking arts includes an earlier invention by one of these inventors (U.S. Pat. No. 4,574,644). When only one sphere is included in the toroidal cavity, this single sphere orbits as long as the velocity of fluid flowing through the toroidal cavity is high enough. However, when the velocity of fluid is low, the single sphere stops orbiting. At best, this embodiment employing a single sphere in a toroidal cavity works as a flow indicator for medium to high flow rates, while it serves little usefulness as a flowmeter or as any other form of the positive displacement fluid handling device. Chagrined by one of these inventor's earlier invention (U.S. Pat. No. 4,574,644) which was nothing more than a helter-skelter Rube Goldberg gadget, this inventor has been brain-storming for the past five years and has finally succeeded in inventing an apparatus that brings forth a very outstanding positive displacement flowmeter capable of measuring very low flow rates of fluid, which apparatus can also provide a motor or pump filling certain niche usages.